How to make a slice in the Particles System?
You can slice them at render time (i.e. the full geometry will still be there, but only the relevant slices will be rendered) by using Material nodes:

Say you want to render only the portion 0.5 &lt; Z &lt; 0.9. Then, as your sphere's material, use a Mix shader:



The Mix Shader should be used to mix your material (whatever that is, e.g. a green Diffuse) and a fully white "Transparent BDSF". 

The mixing "Factor" is either 0 or 1, controlled by a set of "Math" nodes that check whether the "Z" coordinate is in the desired range.

Result:



Note (after your edit): if there are many particles, the "Transmission" value under "Bounces" in the "Light Path" Render settings should be at least twice the number of particles that can be found along a lightpath from your point of view. ← If this doesn't make much sense to you, just increase that value until it looks right.